Basically, when we're talking about individual axes rather than all of them bunched together, it gets more complicated and stuff like "Significance" and "Insignificance" is involved.
Basically, an "Axis" is akin to a line, and two dimensional axes are akin to 2 perpendicular lines. An axis that is an infinite line [both sides extending to infinity] is
significant in size, and that which does not extend to infinity [at which point it's not even a "
Line" other than in name, and is more or rather just a Line segment]] is an
insignificant space.
The best way to explain this is by example. Consider two space-times, we consider the "Space" that separates space-time to be a 4-dimensional space. Not because it's "uncountably infinite times 3D Space" by default, but because "it extends in a different perpendicular direction".
Now, here, we assume that for the 4-dimensional hyperspace, the 3 normal dimensions are, well, significant, but the 4th axis is insignificant [by default, unless proven otherwise] because to prove its significance, there's a need to prove its infinite nature.
Note that, here, by "4-dimensional space", I mean purely spatial dimensions, not counting the time dimension. If we go by order, then the 4th spatial dimension[of this hyperspace] would be the 5th dimension with respect to a space-time.
You may ask, why? Why do we not consider it as infinite by default?
Well, to elaborate, it
is infinite, but only with respect to lower-dimensional beings [any 4D space is infinite in the view of a 3-dimensional being, but not necessarily uncountably infinite]. An example of this is a space-time. While by default, we assume that a space-time's "time dimension" [the fourth dimension by order] is uncountably infinite, which is why we consider it as 4D, because by it being a line/uncountably infinite, it would span a 3D snapshot/structure at each instance/point of time. Since a line has uncountably infinite points, this means an uncountably infinite amount of 3D snapshots are spawned, resulting in 4D.
But what if, for the sake of this explanation, we say that the time dimension is not uncountably infinite? What if its a line segment, and not a line?
Well, a line segment still has infinite points [there can be a point between any two points in a line segment after "zooming" enough]. But there are only a countably infinite amount of points here[just like the set of natural numbers].
Thus, by this, the snapshots spawned by this time dimension would just be a countably infinite amount of 3D structures, thus tiering it at just the high-end of High 3-A, rather than Low 2-C.
This is essentially what applies at the "4th spatial axis, the 5th dimension by geometrical order that separates space-times". However, in this case, we by default assume that its not uncountably infinite, and there is a need for that to be proven.
Hope that explanation was good enough to clear most if not all of your doubts.